Graded Lie algebra

Let $(𝔄, +)$ be a (necessarily abelian) monoid. A $𝔄$ -graded Lie algebra is an example of a graded algebra, #m/def/lie i.e.

[𝐴 𝛼, 𝐴 𝛽] \subseteq 𝐴 𝛼 + 𝛽

Properties